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A normal distribution is a common assumption underlying many statistical tests. Although the assumption is usually not important, it is possible to test whether it is plausible. Specifically, the unit normal table lists proportions for individual sections of a normal distribution, and a chi-square test for goodness of fit can be used to evaluate whether a specific distribution fits the proportions. For example, if a normal distribution is divided into sections using z -score values, then proportions in each section should be as follows: -1.5 < z -0.5 <z 0.5 <z z < -1.5 -0.5 0.5 1.5 z > 1.5 6.68% 24.17% 38.30% 24.17% 6.68% Use these proportions to test whether the following sample of n = 90 scores is significantly different from a normal distribution. Test with a = .05. -1.5 < z -0.5 <z 0.5 <z z < -1.5 -0.5 0.5 1.5 z > 1.5 8 19 31 23 9

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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
Publisher: Cengage Learning
ISBN: 9781133956570
BuyFind

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
Publisher: Cengage Learning
ISBN: 9781133956570

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Chapter
Section
Chapter 15, Problem 7P
Textbook Problem

A normal distribution is a common assumption underlying many statistical tests. Although the assumption is usually not important, it is possible to test whether it is plausible. Specifically, the unit normal table lists proportions for individual sections of a normal distribution, and a chi-square test for goodness of fit can be used to evaluate whether a specific distribution fits the proportions. For example, if a normal distribution is divided into sections using z-score values, then proportions in each section should be as follows:

  -1.5 < z -0.5 <z 0.5 <z  
z < -1.5 -0.5 0.5 1.5 z > 1.5
6.68% 24.17% 38.30% 24.17% 6.68%

Use these proportions to test whether the following sample of n = 90 scores is significantly different from a normal distribution. Test with a = .05.

  -1.5 < z -0.5 <z 0.5 <z  
z < -1.5 -0.5 0.5 1.5 z > 1.5
8 19 31 23 9

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